Particle transport calculations predict the time-dependent spatial density or flux distribution of "freely moving" particles whose motion is influenced only by interaction with other particles and their fields. These calculations have varied applications, such as the design of equipment that controls or utilizes radiation (nuclear reactors, nuclear devices, and medical treatment and diagnostic equipment), the analysis of neutron probe data obtained from geologic exploration, and the modeling of other "particle" systems, such as rarified gases, semiconductors, and vehicular traffic.
One of the main mathematical algorithms used to model the motion of such particles is the transport equation. The transport equation may be solved for complex geometries using numerical methods, in which, for example, the object or system being studied may be modeled as a continuum of discrete cells.
Recent advances in the design and use of multicomputers having parallel processors have allowed calculations for many kinds of models using spatial discretization to be implemented in parallel, which potentially increases the speed at which a solution for these models may be calculated. Nevertheless, the solution of the transport equation has not been optimized for use on a multicomputer parallel processor platform, because the ray tracing sweep used in solving the spatially discretized transport equation has been considered to require strictly serial analysis for the best iteration convergence rates to be achieved.